Loudspeakers

ABSTRACT

A method of making an acoustic member for a loudspeaker having an operative frequency range and acoustic output which depends on the values of parameters of geometry, bending stiffness, areal mass distribution, damping, tension modulus, compression modulus and shear modulus of the member, the method comprising providing an acoustic member having at least one frequency dependent parameter with a variation which depends on frequency, selecting the variation which depends on frequency, selecting the variation of the frequency dependent parameter to effect a desired acoustic output from the loudspeaker and making the member having said selected variation. The method may comprise selecting an acoustic member having a component made from a frequency dependent material which has a glass to rubber transition Tg in the operative frequency range of the speaker.

TECHNICAL FIELD

The invention relates to loudspeakers and more particularly to bendingwave panel-form loudspeakers, e.g. of the kind described in WO97/09842.

BACKGROUND ART

A bending wave loudspeaker typically consists of an acoustic panel andat least one exciter mounted to the panel. The panel may be supported ona frame by a compliant edge termination which isolates the vibratingpanel from the frame. The mechanical properties of the panel, edgetermination and exciter mounting effect the acoustic performance of theloudspeaker.

It is known in the field of bending wave panels that the bending wavebehaviour of a panel may be adjusted by manipulating sets ofco-operative parameters. As taught in WO97/09842, the values of physicalparameters of geometry, bending stiffness, areal mass distribution anddamping of the panel may be selected to effect a desired distribution ofresonant bending wave modes. The panel may be designed to be effectiveover a wide frequency range, maybe up to 8 octaves, by selecting arelatively large panel of good quality materials. However, the bandwidthof a bending wave panel loudspeaker may be limited as a result of theconflicting requirements for achieving good performance at both high andlow frequencies. In general, better high frequency performance isachieved by using a light, stiff panel having low damping and high shearproperties, whereas better low frequency performance is achieved byusing a panel of lower stiffness and higher density.

The high frequency radiation efficiency may be improved by placing thecoincidence frequency in the operative bandwidth of the loudspeaker,even in the lower portion of the operative bandwidth. This may beachieved by ensuring the panel has a high bending stiffness, sincecoincidence frequency is reciprocally proportional to stiffness.However, raising the bending stiffness of the panel reduces the lowfrequency capability of the panel, which may be countered by increasingthe area and/or area mass density of the panel. Alternatively, dampingmay be added to control and smooth the low frequency response,particularly in operative regions where there is low modal density.However, such damping may reduce the output particularly at higherfrequencies.

DISCLOSURE OF INVENTION

Another conflicting requirement which needs to be considered is thedesire to achieve both effective and extended high frequencyperformance. As discussed above, good high frequency performance isachieved by a panel of low density and high stiffness. However, thisresults in a panel having a relatively high mechanical impedance andthus more force is required to drive the panel to a useful loudness.

According to a first aspect of the invention, there is provided anacoustic member for a loudspeaker having an operative frequency range,characterised in that the member comprises a component made from afrequency dependent material having at least one parameter which variesas a function of frequency. The parameter may be selected from the groupconsisting of damping, bending stiffness, tension modulus, compressionmodulus and shear modulus. Since there may be interaction between theparameters, varying one or more parameters may affect other parameters.

The loudspeaker may be a bending wave loudspeaker comprising an acousticradiator which supports bending wave vibration and a transducer mountedby a suspension to the acoustic radiator to excite bending wavevibration in the radiator to produce an acoustic output. The acousticmember may be the acoustic radiator and may be in the form of a panel,for example a distributed mode panel that supports resonant bending wavemodes distributed in frequency over at least part, preferably all, ofthe operative frequency range.

The acoustic member may be a suspension for attaching the loudspeaker ona support, stand or wall and the frequency dependent material may beused to control unwanted vibration from the coupling of the acousticmember on the suspension.

The acoustic member may be a suspension which supports an acousticradiator in a frame or baffle. The suspension may extend around theperimeter of the radiator or may be applied at particular positions onthe radiator. The acoustic member may be the transducer suspension whichsupports the transducer on the acoustic member or may be a transducersuspension which supports the transducer on the frame. For example, thetransducer may be an inertial moving coil exciter having a voice coildirectly bonded to the acoustic radiator frequency-dependent materialand a magnet assembly mounted to the coil by a resilient suspensionwhich may be the component having a frequency dependent parameter.Alternatively, the acoustic member may be in the form of at least onesmall mass mounted on the acoustic radiator, e.g. a mass-loaded polymerfoam pad.

Thus for a bending wave loudspeaker, the acoustic member may be selectedfrom the acoustic radiator, the transducer suspension, the radiatorsuspension or masses mounted on the acoustic radiator. The use offrequency-dependent material is not limited to use as part of the panelof a distributed mode loudspeaker.

The loudspeaker may be a pistonic loudspeaker comprising an acousticradiator in the form of a cone mounted on a frame by a compliant edgetermination, a drive unit supported on the frame by a spider and anenclosure housing the cone and drive unit. The acoustic member may beincorporated in the spider or may be the compliant edge termination.Alternatively, the acoustic member may be the cone or a compliantsuspension which couples the drive unit to the enclosure.

The parameter which varies as a function of frequency may be bendingstiffness and may be lower at low frequencies (i.e. below 1 kHz) than athigh frequencies (above 1 kHz). The bending stiffness is preferably atleast 20% lower at low frequencies than at high frequencies.

For an acoustic member in the form of a bending wave panel, thefundamental frequency (F0) calculated from equation 1 in the appendixgives an approximation to the low frequency limit. Since F0 is directlyproportional to bending stiffness, an acoustic member having lowerstiffness at low frequencies may have an extended low range performancefor a given size.

High frequency performance may also be improved by addressing the known“aperture effect” in which a secondary resonance develops within thediameter of a coil of a moving coil transducer mounted on an acousticradiator. The aperture resonance frequency F_(R) is determined from thebending wave resonance frequency F_(B) and the shear wave resonancefrequency F_(S) using equations 2 to 4 in the appendix.

Since F_(B) and thus F_(R) is dependent on bending stiffness, a bendingwave panel having higher stiffness at higher frequencies may have anaperture resonance frequency occurring at a higher frequency and thusmay have an extended high range performance. Thus, the invention mayprovide a bending wave panel having lower bending stiffness at lowfrequencies and higher bending stiffness at high frequencies whereby abroader frequency range than a member having a constant bendingstiffness is achieved. The bending stiffness may be at least 20% higherat high frequencies (i.e. above 1 kHz) than at lower frequencies (i.e.below 1 kHz). The efficiency of the panel may also be improved incertain regions of the frequency range.

The bending stiffness may rise steadily with increasing frequency andthus may be directly proportional to frequency. Alternatively, thebending stiffness may have a relatively sharp transition at a selectedpoint in the frequency range. In this way, the acoustic member may beconsidered to act as two independent low and high frequency acousticmembers. For example, for an acoustic member in the form of a bendingwave acoustic radiator, the parameters may determine the naturalresonant frequencies and the useable frequency range for the lowfrequency member. Whereas for the high frequency member, the greaterstiffness may allow efficient working to the highest required frequency,and may allow a desired coincidence frequency to be set.

The parameter which varies as a function of frequency may be compliance.For an acoustic member in the form of a compliant edge terminationaround a cone in a pistonic speaker, the termination may have highcompliance at low frequencies and a lower compliance at highfrequencies. In this way, movement of the cone at low frequencies willbe largely unimpeded and simultaneously at higher frequencies, theacoustic energy will be better terminated whereby reflectioninterference may be minimised. The cone may have variable compliance,for example by appropriate choice of the polymer blend or by treatingthe cone after manufacture. The cone may have high damping at lowfrequency and enhanced stiffness at higher frequencies which may be usedto enhance speaker performance. The damping may be at least 20% higherat high frequency than at low frequency and the stiffness may be atleast 20% greater at high frequency than at low frequency.

It is known that the use of a compliant suspension between the coil andmagnet assembly of the transducer of a bending wave speaker may lead toa transducer resonance in the low frequency range of the speaker. Thisis known as the inertial resonance. The compliant suspension may havehigh damping whereby the amplitude of the resonance may be broadenedand/or the resonance may be selectively tuned to a specific frequency.In this way, improved low frequency performance may be achieved.Similarly, the damping of the compliant transducer suspension betweenthe transducer and the frame may be selected to broaden the amplitude ofor change the frequency of this fundamental resonance of the transducer.

The parameter which varies as a function of frequency may be damping.The damping of a material may be dependent on the chemistry, polymerformation and/or specific loss mechanisms within the material. Thedamping may rise or fall with increasing frequency whereby refinement ofacoustic performance may be achieved. The damping may be applied overall or part of the acoustic member. EP 0 621 931 B1 describes the use ofdamping materials which have high damping factors at specifictemperature ranges and such material may be altered to have dampingwhich varies as a function of frequency.

An acoustic member in the form of a mass may be positioned to couple tospecific mode(s) in an acoustic radiator. The mass may have high dampingat low frequency and low damping at high frequency whereby a specificlow frequency resonant mode may be effectively damped without greatlyeffecting high frequency resonant modes. A similar effect may beachieved by using an acoustic member in the form of an acoustic radiatorhaving frequency dependent material applied at specific positions insidethe structure of the acoustic radiator, e.g. at the transducer location.For example, the acoustic radiator may comprise a honeycomb core havingfrequency dependent material injected into specific cells.Alternatively, the surface of the acoustic member may have regions offrequency dependent material which may be arranged in rectangular,triangular or polygonal block format or in a concentric format.

An acoustic member in the form of a bending wave acoustic radiator mayhave a higher level damping, i.e. at least 20% greater, at a particularfrequency whereby the distribution of modes around that particularfrequency is improved. Increasing the damping results in broaderresonant modes which may distribute the modes more evenly in frequency.Thus, a smoother response may be obtained around that particularfrequency.

The acoustic member may comprise more than one frequency dependentparameter. For example, an acoustic member in the form of a radiatorsuspension extending around the perimeter of a bending wave acousticradiator may have low damping and low compliance at higher frequenciesand high damping and high compliance at lower frequencies. Increasingthe level of damping may broaden the low frequencies modes and may thusimprove modal spread at low frequencies. Increasing the level of dampingmay also increase the absorption of bending wave vibration at theboundary. This may be particularly useful for an acoustic radiator whichhas low damping since this may control reverberation of the radiator. Byincreasing the compliance at low frequencies, the acoustic radiator maybe generally freely suspended and the low frequency modes of theacoustic radiator are shifted to lower frequencies. By decreasing thecompliance at high frequencies, the acoustic radiator may be generallyclamped or boundary terminated whereby the high frequency modes of theacoustic radiator are shifted to lower frequencies.

The effect and advantages of clamping and boundary termination areexplained in WO99/52324 to New Transducers Ltd. However, edge controlcan also reduce the low frequency output. Thus, by using afrequency-dependent material, an advantageous combination of propertiescan be obtained.

The acoustic member may be a composite structure comprising at least twocomponents. Only one component or alternatively all components in thecomposite structure may have a frequency dependent parameter. In thisway, the parameters of the components individually or in combination maybe selected to enhance performance. For example, the acoustic member mayhave a sandwich or laminate construction. Thus the member may comprise acore of low density material (e.g. foam or honeycomb) and two skinsadhered by adhesive layers to opposed faces of the core. The core, skinsand/or adhesive layer may be made from a frequency dependent materialhaving a frequency dependent parameter. The skins may be sprayed on orapplied as a continuous film.

One advantage of using skins having frequency dependent parameter may beto counteract shear effects in some core materials. Such shear effectsmay significantly reduce the overall bending rigidity of the structureat high frequency and thus may limit performance in this bandwidth.Thus, by choosing skins which have bending stiffness increasing withfrequency, rigidity of the panel may be maintained and thus highfrequency performance may be improved.

Alternatively, the acoustic member may be a monolithic structure, i.e.one not being of core and skin construction, e.g. a structure made fromsolid polymers (e.g. polycarbonates, acrylics, polyesters), foamedplastics, metal, wood or felted paper. The monolithic structure may bemade of frequency-dependent material which has a frequency dependentparameter.

For a monolithic panel, bending stiffness is directly proportional tothe Young's modulus as set out in equation 5 in the appendix. Thus thefrequency dependent parameter may be the Young's modulus (hereinaftermodulus) of the frequency dependent material. Thus, as described above abroader bandwidth for an acoustic panel may be achieved by using amaterial which has a modulus which is lower at low frequency and higherat high frequency. The expression for bending stiffness for a compositestructure, e.g. sandwich panel, is more complex but is still dependenton the modulus and thus modulus may be the frequency dependentparameter.

The acoustic member may comprise a surface layer having a frequencydependent parameter. The surface layer may be applied either as a spraycoating or a film layer and may act as an anti-reflection coating fortransparent applications. The surface layer may be applied to monolithicor sandwich members.

The frequency dependent material may be a viscoelastic material, i.e. amaterial possessing time-dependent properties. For example, viscoelasticmaterials have previously been used for vibration damping, acousticattenuation or isolation purposes. Such materials and their methods ofmanufacture are, for example, described in WO93/15333 to MinnesotaMining and Manufacturing Company. Many viscoelastic materials havemechanical properties which change with frequency excitation and maythus be designed to have maximum energy absorption at a specificfrequency.

The frequency dependent material preferably has a glass to rubbertransition in which damping of the material has a sharp peak and storagemodulus of the material drops by several, e.g. three, orders ofmagnitude. Such a transition may be regarded as critical in creating adegree of frequency dependence in the material. The transitionpreferably occurs in the operative frequency range of the speakerwhereby energy absorption or damping may be maximised. The transitionmay occur in the temperature range −20° C. to 50° C. and at frequenciesbetween 0.1 Hz to 1 kHz. The acoustic member may have separate regionseach having transitions at different frequencies.

The frequency dependent material may be a resin e.g. polyurethane orepoxy, with a glass-to-rubber transition at a frequency within therequired frequency range, whereby the material has low modulus orstiffness at low frequencies but higher modulus at higher frequencies.For an acoustic member in the form of a panel this should beneficiallydecrease the frequency of the lowest operational mode of the panelwhilst enhancing the stiffness of the panel at higher frequencies.

The frequency dependent material may be a thermoplastic polymer havingdamping and/or other mechanical properties which depend on temperatureand/or frequency. The frequency dependent material may be a foamedmaterial, whereby a low density material with variable dampingproperties may be achieved. The foamed material may be used as a core oras small individual damping masses placed on another surface. Thefrequency dependent material may be a polymer blend from which theacoustic member is manufactured by injection moulding or extrusion.

The frequency dependent material may be used in combination with anon-frequency dependent material. The frequency dependent material maybe a polymeric material which encapsulates a higher modulus fibrereinforcement such as carbon or glass fibres. Changes in the modulus ofthe polymeric material may result in a change of the overall modulus ofthe acoustic member which depends on the proportions of the fibre to thepolymeric material and their relative properties. Alternatively, thepolymeric material may encapsulate metal or ceramic, whereby theacoustic member may benefit from the high mass of the metal or ceramicand the variable damping of the polymeric material.

The acoustic member may be in the form of an acoustic radiator and maytaper across its width and/or its length. The thickness of the radiatormay increase or decrease from its centre to its perimeter. By decreasingthe thickness, the central region of the acoustic radiator may be stiffand act as a bending wave acoustic radiator and the edge region may havehigher compliance whereby the acoustic radiator may be mounted directlyto a supporting frame, i.e. without a separate edge suspension. Asimilar effect may be achieved by other mechanisms which vary themodulus across the acoustic radiator.

The use of frequency dependent materials provides another parameterwhich may be used to improve performance of a speaker. Thus, accordingto a second aspect of the invention, there is provided a method ofmaking an acoustic member for a loudspeaker having an operativefrequency range and acoustic output which depends on the values ofparameters of geometry, bending stiffness, areal mass distribution,damping, tension modulus, compression modulus and shear modulus of themember, the method comprising providing an acoustic member having atleast one frequency dependent parameter with a variation which dependson frequency, selecting the variation of the frequency dependentparameter to effect a desired acoustic output from the loudspeaker andmaking the member having said selected variation.

The acoustic member may be selected to have a component made from afrequency dependent material which has a glass to rubber transitionwhich preferably occurs in the operative frequency range of the speaker.The method may comprise modifying the frequency dependent material toadjust the temperature and/or frequency at which the transition occurs.The material may be a polymer and modifying the material may comprisemodifying at least one of the parameters in the group consisting ofmolecular weight, (i.e. sum of the weight of all the atoms in a moleculedivided by the number of molecules in a polymer), moleculardistribution, steric effects (i.e. effects of side groups attached topolymer chain), polarity of side group and crosslink density. Aplasticizer may be added to the polymer to lower the transitiontemperature.

The molecular weight may be increased to increase the transitiontemperature or vice versa. The distribution may be altered to increasethe tendency to cause entanglement i.e. wrapping of chains around eachother, and hence to increase the transition temperature or vice versa.Attaching a bulky or complex side group may increase the transitiontemperature or vice versa. For example substituting the hydrogen sidegroup in Poly(cis-1,4)butadiene with a methyl group to give naturalrubber (Poly(cis-1,4)isoprene) raises the transition temperature from−108° C. to −73° C.

Replacing a side group with an appropriately polarised (i.e. negative orpositive) side group may increase secondary bonding with the main chainand hence increase the transition temperature or vice versa. Forexample, replacing the methyl group in natural rubber with a chlorineatom gives Polychloroprene (Neoprene®) and increases the transitiontemperature from −123° C. to −50° C., even though the methyl group islarger. These principles may be applied to design polymers which show atransition temperature having a value close to room temperature, i.e.above 21° C.

In some polymeric materials two adjacent molecules may form a strongbond, i.e. may be cross-linked. By increasing the number of and hencedensity of cross-links, the transition temperature may be raised orvice-versa. The control of cross-linking in polymers applies to allpolymers which exhibit cross-linking, including a range of boththermoset and thermoplastic materials e.g. polyurethanes, epoxy resins,polyesters (unsaturated and saturated), bismaleimide resins, phenolics,vinyl esters.

The polymer may have regions of amorphous and crystalline structure,i.e. regions having a random entanglement of molecules and regions ofregularly-packed, repeatable molecules, respectively. Such a polymer mayhave two transition temperatures, namely a glass transition and acrystalline melting temperature at which temperature the bonds in thecrystalline structure break down. By adjusting the parameters of theregions having an amorphous structure, the transition temperature may beadjusted, provided the glass transition temperature remains lower thanthe melting point.

The polymer may be a copolymer consisting of two distinct monomers e.g.polypropylene and polyethylene. The transition temperature and/orfrequency may be adjusted by altering the relative proportions of thetwo monomers and/or by arranging the two monomers in different ways,e.g. in alternating structure or in blocks of each monomer type, etc.The co-polymer may combine several different polymers each with highdamping characteristics at different temperatures. Polymers which showhigh damping properties are described in the following reference NielsenL. E. “Mechanical Polymers”.

Some small amplitude non linearities may result from the use of suchfrequency dependent materials which needs to be considered by aloudspeaker designer.

BRIEF DESCRIPTION OF DRAWINGS

For a better understanding of the invention, and purely by way ofexample, specific embodiments of the invention will now be describedwith reference to the accompanying drawings, in which

FIG. 1 illustrates a distributed mode loudspeaker according to theinvention;

FIG. 2 is a graph showing the variation in Young's modulus withfrequency for the loudspeaker of FIG. 1 compared with a loudspeaker madeaccording to the prior art;

FIG. 3 is a frequency response (acoustic pressure in dB againstfrequency Hz) for the loudspeakers of FIG. 2;

FIG. 4 a graph of stress σ and strain ε against sinusoidal force ωt fora material;

FIG. 5 is a graph showing both variation in storage modulus (log E′) anddamping factor (d_(E)) against temperature which illustrates the glassto rubber transition;

FIG. 6 is a graph showing log of frequency against the inverse oftemperature for a polymer;

FIG. 7 is a graph showing variation in storage modulus (log E′) anddamping factor (d_(E)) against temperature for two differentfrequencies, and

FIG. 8 which is a graph of showing the variation of damping and storagemodulus with frequency.

BEST MODES FOR CARRYING OUT THE INVENTION

Referring to FIG. 1, a panel 11 is shaped to have a distribution ofresonant bending wave mode in an operative frequency range of interest.The values of the parameters of the panel are chosen to smooth peaks inthe frequency response caused by “bunching” or clustering of the modes.The resultant distribution of resonant bending wave modes, particularlylow frequency modes, may thus be such that there are substantiallyminimal clusterings and disparities of spacing. The resonant bendingwave modes associated with each conceptual axis of the panel-form memberare arranged to be interleaved in frequency whereby a substantially evendistribution may be achieved.

A transducer 13 is provided on the panel at a location for coupling wellto the resonant bending wave modes, as described in WO97/09842, namelyat a position (4/9L_(x), 3/7L_(y)). Thus the transducer is at a locationwhere the number of vibrationally active resonance anti-nodes isrelatively high and conversely the number of resonance nodes isrelatively low. The transducer is an electrodynamic exciter with a voicecoil having a diameter of 25 mm.

The panel is a monolith made from PolyMethylMethacrylate (n-butyl) PMMAwhich is a material having a glass to rubber transition temperatureT_(g) of 27° C. Thus the transition from glassy to rubbery behaviourbegins to occur at room temperature (25° C.). The effect of such atransition is explained with reference to FIGS. 4 to 6. The parametersof the material are set out in the table below together with theparameters of polycarbonate which was used to make a second panel withthe same dimensions, same transducer placement and same transducer typefor comparative purposes. Material Polycarbonate PMMA Density (ρ) kg m⁻³1200 1160 Young's Modulus (E) GPa 2.3 1.9 Damping Factor (d_(E)) @ 5 kHz0.011 0.051 Glass Transition Temperature 118 27 (T_(g)) ° C.

FIG. 2 shows the variation 43, 41 in Young's modulus with frequency forthe loudspeakers made from PMMA and polycarbonate, respectively. Thevalue of Young's modulus E is calculated by measuring the bending wavevelocity c_(B) for each frequency and by applying equation 6.

FIG. 2 shows that the rate of increase of Young's modulus with frequencyis greater for the PMMA panel than for the polycarbonate panel eventhough the polycarbonate panel has a greater static value of Young'smodulus (2.3 GPA compared with 1.9 GPA). Thus, the PMMA panel has ahigher Young's modulus at high frequencies than at low frequencies andhas a higher Young's modulus at high frequencies than the polycarbonatepanel.

FIG. 3 shows the frequency responses 47, 45 for the loudspeaker usingthe PMMA panel and polycarbonate panel respectively. The apertureresonance for the loudspeaker using the PMMA panel occurs at a higherfrequency than the aperture frequency for the loudspeaker using the PMMApanel, approximately 18.1 kHz compared to 16.04 kHz. Thus, the PMMApanel provides an increased high frequency limit compared to thepolycarbonate panel which has a lower rate of increase of modulus withfrequency.

The PMMA panel has static values for Young's modulus and density whichare approximately 13% lower than the values for the polycarbonate panel.Thus, the modal frequencies would be expected to be correspondinglylower. However, as shown in FIG. 3, the local modal frequency for thePMMA panel is higher than for the polycarbonate panel which results fromthe greater change in Young's modulus with frequency for PMMA than forpolycarbonate.

FIG. 4 shows the sinusoidal variation 15, 17 of the stress (σ) andstrain (ε) in a viscoelastic material respectively as well as the phaselag parameter (δ) between the stress and strain components. The time lagcomponent may be used to derive the damping or loss factor (η) as shownin Equation 7. Equation 7 also shows the relationship between thestorage modulus E′ and the loss modulus E″ which represents thecapability of the material to store or lose energy respectively andwhich are the real and imaginary parts of the complex Young's modulusrespectively. The damping factor controls the degree of absorption ofenergy and is a material parameter which does not vary with dimensionsfor an isotropic homogeneous material. The complex Young's modulusdetermines the rigidity of a component.

FIG. 5 shows the variation of damping factor 19,21 d_(E) and storagemodulus E′ with temperature respectively for a thermoplastic polymermaterial at a fixed frequency. At low temperatures, i.e. below T₀, thematerial exhibits glassy behaviour. The material is stiff with a highstorage modulus and a generally constant low damping factor. At highertemperatures, i.e. above T₁, the material exhibits rubbery behaviour.The material is more compliant, has a low storage modulus and agenerally constant low damping factor. As the temperature increasesfurther, i.e. above T₂ the material begins to flow.

The glass to rubber transition occurs between the temperatures To andT₁. During the transition there is a sharp drop in the value of thestorage modulus and the damping factor rises sharply to a peak thenfalls sharply away. The maximum value of the damping factor occurs atthe glass transition temperature T_(g). At this temperature, the strainlags behind the stress by exactly the amount to cause maximum energydissipation.

The variation of storage modulus with temperature may be equated to thatof storage modulus with frequency. High temperatures are equivalent tolow frequencies and high frequencies are equivalent to low temperatures.

The frequency at which the glass transition temperature occurs may beshifted from a reference frequency f₀ to another frequency f accordingto equation 8. Equation 8 may be rearranged and by plotting a graph oflog f against the inverse of temperature as shown in FIG. 6. Theactivation energy for each transition process may be derived from thegradient of the graph. Since the graph has a constant gradient, theactivation energy is constant, although this is only correct in thetransition period. Thus, if the frequency is shifted from F₀ to a higherfrequency F₂, there is a corresponding increase in the transitiontemperature from T₀ to T₂. If the frequency is decreased to F₁, there isa corresponding decrease in the transition temperature to T₁.

A shift in the frequency affects the storage modulus E′ and the dampingfactor d_(E). This is illustrated in FIG. 7 which shows the variation23,25 in storage modulus E′ at frequency F₀ and F₂ respectively and thevariation 27,29 in damping factor d_(E) at frequency F₀ and F₂respectively. By shifting the transition temperature T_(g) to a highervalue, the value of the storage modulus is higher at any operatingtemperatures.

The change in damping factor is more complicated and shifting thetransition temperature T_(g) to a higher value may lead to an increasingor decreasing damping factor depending on the operational temperature.At the operational temperature of T₃ the damping factor for thefrequency F₂ is lower than for F₀ and is constant rather than increasingin value. However, at the operational temperature of T₄, the values ofthe damping factor are approximately equal but the damping factor isdecreasing for F₀ and increasing for F₂.

This is illustrated in FIG. 8 which is a graph showing the variation29,31 and 33 of damping and storage modulus with frequency. The dampingmay decrease with frequency as illustrated by variation 29 or mayincrease with frequency as illustrated by variation 31. The storagemodulus increase with frequency as shown by variation 33. Thus, thereare two possible options for the damping behaviour and stiffness of apanel manufactured using these materials:

Low stiffness/high damping at low frequencies but high stiffness/lowdamping at high frequencies.

Low stiffness/low damping at low frequencies but high stiffness/highdamping at high frequencies.

Thus by changing the transition temperature or frequency for aparticular polymer, the mechanical properties may be modified to achievespecific values of storage modulus and damping. These materials havingdesigned variations in performance with frequency may be used to makepanels and related components for acoustic devices and loudspeakerswhereby improvements in frequency bandwidth and performance may beachieved.

APPENDIX

$\begin{matrix}{{F0} = {\frac{\pi}{A}\sqrt{\frac{B}{\mu}}}} & {{Equation}\quad 1}\end{matrix}$where

-   F0: fundamental frequency (Hz)-   A: panel area (m²)-   B: average bending rigidity or stiffness (Nm)=½(B_(x)+B_(y))-   μ: areal/surface density (kg m⁻²) $\begin{matrix}    {F_{B} = {\frac{1}{2\pi}( \frac{4.81}{D_{E}} )\sqrt{\frac{B}{\mu}}}} & {{Equation}\quad 2}    \end{matrix}$    where-   F_(B): bending wave resonance frequency-   D_(E): exciter diameter $\begin{matrix}    {F_{S} = {\frac{1}{2\pi}( \frac{4.81}{D_{E}} )\sqrt{\frac{Gt}{\mu}}}} & {{Equation}\quad 3}    \end{matrix}$    where:-   F_(S): shear wave resonance frequency-   G: through thickness shear modulus $\begin{matrix}    {F_{R} = \sqrt{\frac{F_{B}^{2}F_{S}^{2}}{F_{B}^{2} + F_{S}^{2}}}} & {{Equatio}\quad n\quad 4}    \end{matrix}$    where:-   F_(R): cumulative resonant frequency $\begin{matrix}    {B = \frac{E\quad t^{3}}{12( {1 - v^{2}} )}} & {{Equation}\quad 5}    \end{matrix}$    where:-   B: bending stiffness-   t: thickness-   E: Young's modulus (Pa)-   v: Poisson's ratio $\begin{matrix}    {c_{B} = {\sqrt{\omega}\sqrt{\frac{B}{\mu}}}} & {{Equation}\quad 6}    \end{matrix}$    where-   C_(B): bending wave velocity (m s⁻¹)-   ω: frequency (rads)-   B: bending rigidity (Nm)-   μ: areal density (kg m⁻²) $\begin{matrix}    {\eta = {{\tan\quad\delta} = \frac{E^{''}}{E^{\prime}}}} & {{Equation}\quad 7}    \end{matrix}$    where-   E′: storage modulus/real modulus (GPa)-   E″: loss modulus/imaginary modulus (GPa)-   δ: phase lag parameter-   η: damping or loss factor $\begin{matrix}    {f = {f_{0}{\exp( \frac{{- \Delta}\quad H}{R\quad T} )}}} & {{Equation}\quad 8}    \end{matrix}$    where-   f frequency (Hz)-   f₀ frequency constant for material (Hz)-   ΔH activation energy for process-   R gas constant-   T temperature (° K)

1. A method of making a bending wave acoustic radiator for aloudspeaker, the acoustic radiator having a bending stiffness whichvaries with frequency, the method comprising selecting the variation ofthe bending stiffness such that the bending stiffness is lower at lowfrequencies and higher at high frequencies to effect a desired acousticoutput from the loudspeaker, and making the acoustic radiator havingsaid selected variation.
 2. A method according to claim 1, comprisingselecting an acoustic radiator having a component made from a frequencydependent material which has a glass to rubber transition in theoperative frequency range of the speaker.
 3. A method according to claim2, comprising modifying the frequency dependent material to adjust thefrequency at which the transition occurs.
 4. A method according to claim3, wherein the material is a polymer and the method comprises modifyingat least one of the parameters in the group consisting of molecularweight, molecular distribution, steric effects, polarity of side groupand crosslink density.
 5. A method according to any one of claims 1 to4, comprising selecting the variation in bending stiffness to have arelatively sharp transition at a selected point in the frequency range.6. A method according to claim 5, wherein the frequency dependentmaterial is selected from the group consisting of viscoelastic material,resins, thermoplastic polymers, foamed material and polymer blends.
 7. Amethod according to claim 6, wherein the frequency dependent material isa polymeric material which encapsulates a fibre reinforcement having ahigher modulus which is independent of frequency.
 8. A method accordingto claim 7, wherein the frequency dependent material is a polymericmaterial which encapsulates a second material having a higher mass whichis independent of frequency.
 9. A method according to any one of claims1 to 4, wherein the frequency dependent material is selected from thegroup consisting of viscoelastic material, resins, thermoplasticpolymers, foamed material and polymer blends.
 10. A method according toclaim 9, wherein the frequency dependent material is a polymericmaterial which encapsulates a fibre reinforcement having a highermodulus which is independent of frequency.
 11. A method according toclaim 10, wherein the frequency dependent material is a polymericmaterial which encapsulates a second material having a higher mass whichis independent of frequency.
 12. A method of making an acoustic memberfor a loudspeaker having an operative frequency range and an acousticoutput which depends on the values of physical parameters of the memberthat include damping, the acoustic member being in the form of acompliant suspension between a coil and magnet assembly of a moving coiltransducer, the suspension having a damping which varies with frequency,the method comprising selecting the damping to have a high value at aspecific frequency whereby a resonance at that specific frequency isdamped, and making the member having said selected variation of damping.13. A method of making an acoustic member for a loudspeaker having anoperative frequency range and an acoustic output which depends on thevalues of physical parameters of the member that include damping, theacoustic member being in the form of a mass coupled to at least oneresonant bending wave mode in an acoustic radiator, the mass having adamping which varies with frequency, the method comprising selecting thedamping of the mass to be high at low frequency and low at highfrequency, and making the member having said selected variation ofdamping.
 14. An acoustic member for a loudspeaker having an operativefrequency range, wherein the member comprises a component made from afrequency dependent material having at least one parameter which variesas a function of frequency.
 15. An acoustic member according to claim14, wherein the parameter is selected from the group consisting ofdamping, bending stiffness, Young's modulus, tension modulus,compression modulus and shear modulus.
 16. An acoustic member accordingto claim 14 or claim 15, having a composite structure comprising atleast one component having a frequency dependent parameter.
 17. Anacoustic member according to claim 16, comprising a core of low densitymaterial and two skins adhered by adhesive layers to opposed faces ofthe core, the skins having stiffness increasing with frequency.
 18. Anacoustic member according to claim 14, wherein the acoustic member is asuspension for attaching the loudspeaker on a support, stand or wall.19. An acoustic member according to claim 14, wherein the loudspeaker isa bending wave loudspeaker comprising an acoustic radiator whichsupports bending wave vibration and a transducer mounted by a suspensionto the acoustic radiator to excite bending wave vibration in theradiator to produce an acoustic output and the acoustic member isselected from the group consisting of the acoustic radiator, thetransducer suspension, a suspension which supports the radiator in aframe or masses mounted on the acoustic radiator.
 20. An acoustic memberaccording to claim 19, wherein the acoustic member is a bending waveacoustic radiator having lower bending stiffness at low frequencies andhigher bending stiffness at high frequencies.
 21. An acoustic memberaccording to claim 20, wherein the bending stiffness has a relativelysharp transition at a selected point in the frequency range.
 22. Anacoustic member according to claim 19, wherein the transducer is amoving coil transducer having a coil and magnet assembly and theacoustic member is in the form of a compliant suspension between thecoil and magnet assembly and has high damping at a specific frequencywhereby a resonance at that specific frequency is damped.
 23. Anacoustic member according to claim 19, wherein the acoustic radiator hasa distribution of resonant bending wave modes and the acoustic member isin the form of a mass coupled to at least one specific mode in theacoustic radiator, the mass having high damping at low frequency and lowdamping at high frequency.
 24. An acoustic member according to claim 19,in the form of an acoustic radiator having frequency dependent materialapplied at specific positions inside the structure of the acousticradiator.
 25. An acoustic member according to claim 19, in the form of aradiator suspension extending around the perimeter of a bending waveacoustic radiator, the suspension having low damping and low complianceat higher frequencies and high damping and high compliance at lowerfrequencies.
 26. An acoustic member according to claim 19, in the formof a monolithic bending wave panel formed from a material having aYoung's modulus which is lower at low frequency and higher at highfrequency.
 27. An acoustic member according to claim 19, in the form ofan acoustic radiator which tapers across at least one dimension.
 28. Anacoustic member according to claim 27, wherein the central region of theacoustic radiator is stiff and the edge region has higher compliancewhereby the acoustic radiator acts both as an acoustic radiator and anedge suspension to a supporting frame.
 29. An acoustic member accordingto claim 14, wherein the loudspeaker is a pistonic loudspeakercomprising an acoustic radiator in the form of a cone mounted on a frameby a compliant edge termination, a drive unit supported on the frame bya spider and an enclosure housing the cone and drive unit and theacoustic member is selected from the group consisting of the spider, thecompliant edge termination, the cone or a compliant suspension whichbonds the drive unit to the enclosure.
 30. An acoustic member accordingto claim 29, in the form of the compliant edge termination around thecone, the termination having high compliance at low frequencies and alower compliance at high frequencies.
 31. An acoustic member accordingto claim 29, in the form of the cone and having high damping at lowfrequency and enhanced stiffness at higher frequencies.
 32. An acousticmember according to claim 14, wherein the frequency dependent materialhas a glass to rubber transition in the operative frequency range of thespeaker.
 33. An acoustic member according to claim 32, wherein theacoustic member has separate regions each having transitions atdifferent frequencies.
 34. An acoustic member according to claim 14,wherein the frequency dependent material is selected from the groupconsisting of viscoelastic material, resins, thermoplastic polymers,foamed material and polymer blends.
 35. An acoustic member according toclaim 14, wherein the frequency dependent material is a polymericmaterial which encapsulates a fibre reinforcement having a highermodulus which is independent of frequency.
 36. An acoustic memberaccording to claim 14, wherein the frequency dependent material is apolymeric material which encapsulates a second material having a highermass which is independent of frequency.